EINSTEIN AND THE

THEORY OF

RELATIVITY

Dual Nature of Light

• Einstein understood that light traveled very

fast, and as a wave, as demonstrated by

experiments.

• He also knew from his own work that it

traveled as a particle. (The Photoelectric

Effect.)

• Scientists considered light traveled like

sound in a medium.

The Medium

• Scientists also thought that light traveled

through a medium which filled space.

• This medium was called ether.

• Several scientists set out to find this ether.

• The most famous experiment was done by

two American scientists, Albert A.

Michelson and Edward W. Morley, in 1887.

Michelson-Morley Experiment

• Michelson and Morley stated that the ether

remained “fixed” in the universe.

• As Earth moved through the ether, it would

give rise to an “ether wind”.

Speed of Sound in Air

• Like sound in air, if air moves, the speed of

sound also changes.

Airplane Analogy

• When equal round-

trip distances are

flown as shown, the

trip parallel to the

wind always takes

longer.

Same Properties for Light

• Replace ether for the wind, and light for the airplanes, then light would return at different times.

• Light detected would be different at 90 degree angle.

Michelson-Morley Experiment

• Michelson-Morley Experiment animation

The Results

• Michelson and Morley found no change in the speeds of light. Both light trips returned at exactly the same time, every time.

• Their conclusion was that there was no ether.

• Michelson especially did not believe this.

• This conclusion caused quite a stir in the world of Physics.

The Results

• Show the Movie “The Michelson – Morley

Experiment” from The Mechanical Universe

Series, #41.

Albert Einstein

• In 1905, Einstein published his Special

Theory of Relativity, which explained the

results of the Michelson-Morley

Experiment.

• This theory was rejected by many

scientists.

• It required some thinking that went against

“classical common sense.”

The Special Theory of Relativity

• This special theory has two postulates.

• A postulate is (logic) a proposition that is

accepted as true in order to provide a basis

for logical reason.

• Postulate 1 – The Principle of Relativity –

All laws of physics are the same for all

observes moving at a constant velocity with

respect to one another.

The Special Theory of Relativity

• So, in other words, All physics works for

everyone with the same motion, whether at

rest or in motion, and

• You cannot tell if you are at rest or in

motion.

Postulate 1

• The laws of nature are the same in a

laboratory at rest as they are in any

uniformly moving laboratory.

• Everything would appear the same.

Postulate 1

• Suppose a person is watching uniformly

moving cars. The velocities are shown in

reference to the ground or the stationary

observer.

Postulate 1 • If car A is taken as a reference system, car B is not moving and car C is moving with a speed of 10 km/hr.

• With respect to car A, the “stationary” observer is moving with a speed of 40 km/h in the direction opposite to that of car C.

• Hence the motion is relative.

Postulate 1 • But, in relation to Car C, Car A and B are moving

backwards at 10 km/h, and the man is also

moving backwards at 50 km/h.

• So, it depends on where you are!!!!

Postulate 1

• What all this means is that there is no

“absolute” reference frame with the unique

property of being at rest with respect to

everything else,

• Like the ether,

• So Einstein says the concept of ether is

rejected.

Postulate 2

• Speed of light in free space is the same for all observers – regardless of motion of the observer.

• Velocity is constant for any observer, even if the object is moving, no matter the direction.

• The speed of light is not added or subtracted, like sound in the wind example.

Postulate 2

• Classically, the thrown ball has a velocity

relative to the moving thrower, and the

velocity of the ball is different for an

observer in another system.

Postulate 2 • Relativistically, light has the same speed for all observers.

• The speed of light for the man on the train is c.

• The speed of light for the man on the ground is c.

Time Dilation and Length Contraction

• Two of the “strange” predictions of the

special theory involved the measurement of

time and length, also mass.

• We do not notice it in our world because we

are moving so slow as compared to the

speed of light.

• When speeds approach the speed of light,

then the difference becomes noticeable.

Time Dilation and Length Contraction

• The special theory predicts that an observer will measure different times and lengths in the different systems.

• That is, when an observer compares times and lengths that he measures to his own, he finds they are different.

• A clock in a moving system will move slower and the measured lengths will be shorter.

Proof • Must have fast moving particles.

• Scientists have used muons, which have

the same charge as an electron, but have

200 times the mass.

• Muons are created in the upper

atmosphere as a result of the collision of

cosmic ray with the nuclei of the gas

molecules of the air.

• The muons then approach the Earth with

speeds near the speed of light. (~0.998c)

Proof

• Muons are unstable and quickly decay.

• The average life span of a muon in the lab is 2

microseconds.

• Moving at this speed, the muon would travel only

600 meters.

• Muons are created in the upper atmosphere

(several kilometers) and many scientists thought

they would not reach the earth’s surface.

• Yet many actually reach the earth’s surface.

Proof

• The muon decays by its own clock and not

by ours on earth.

• Figuring in time dilation on the moving

muon, and the muon measuring its own 2

microseconds, the muon “clock” runs more

slowly.

Proof

• Using an equation,

the time on earth is

measured as 30

microseconds for

the life of a muon.

• During this time, the

muon actually

moves about 9000

meters or 9 km.

Proof

• This is close enough to

reach the Earth’s surface.

• The muon measures it

own distance to be 530 m

during its 2 microsecond

lifetime.

The Twin Paradox

• The “twin paradox” states the problem in terms of a set of twins.

• Suppose one of the twins takes a high-speed space journey that takes 40 years according to the twin who stays on Earth.

• If the space traveling twin travels at .95c, the Earth twin would spend 40 years observing the 10 years that elapsed on the spaceship clock.

The Twin Paradox

• If the twins were 25

years old at blast-

off, then the space

traveler is 35 years

old on return and

his brother is 65.

Twin Paradox - Tested

• Not with real twins, now really, but with

atomic-clock twins.

• Cesium atomic clocks, four of them, were

flown around the world in opposite

directions on commercial aircraft in 1972.

• The clocks were previously synchronized

with stationary cesium-clock twins on earth.

Twin Paradox - Tested • Afterward, the moving clocks were “out of

sync” with the stationary clocks.

• The flying clocks came back “younger”.

• Experiments with unstable particles

accelerated to high speeds in a particle

accelerator provide data that shows the

accelerated particles live longer than their

unaccelerated twin.

• When the relativity formulas are used, it

accounts for the time difference.

The General Theory of Relativity

• Ten years after putting forth the Special

Theory of Relativity, Einstein did it again.

• He put forth his General Theory of

Relativity.

• This theory expanded the math from

relativistic applications to accelerated

systems.

The General Theory of Relativity

• Einstein was intrigued by the fact that the two ways of measuring mass come up with the same value.

• In Newton's second law of motion, an object's mass is measured by seeing how much it resists a change in motion (its inertia).

• In Newton's law of gravity, an object's mass is determined by measuring how much gravity force it feels.

• The fact that the two masses are the same is why Galileo found that all things will fall with the same acceleration.

The General Theory of Relativity

• He proposed an experiment involving two

elevators: one at rest on the ground on the

Earth and another, far out in space away

from any planet, moon, or star, accelerating

upward with an acceleration equal to that of

one Earth gravity (9.8 meters/second2).

(Modern readers can substitute ``rocket

ship'' for Einstein's elevator.)

The General Theory of Relativity

• If a ball is dropped in the elevator at rest on the Earth, it will accelerate toward the floor with an acceleration of 9.8 m/s2.

• A ball released in the upward accelerating elevator far out in space will also accelerate toward the floor at 9.8 m/s2.

• The two elevator experiments get the same result!

The General Theory of Relativity

• Einstein used this to formulate the

equivalence principle that would be the

foundation of General Relativity.

• It states that ``there is no experiment a

person could conduct in a small volume of

space that would distinguish between a

gravitational field and an equivalent uniform

acceleration''.

The General Theory of Relativity

• A consequence of this is that if an elevator is falling freely toward the ground because of gravity, an occupant inside will feel weightless just as if the elevator was far away from any planet, moon, or star.

• No experiment would help you distinguish between being weightless far out in space and being in free-fall in a gravitational field.

The General Theory of Relativity

• According to Einstein’s general theory, the

principle of equivalence holds not only for

mechanical phenomena, such as in

dropping an object, but for all phenomena,

including electromagnetic phenomena.

(Light waves)

The General Theory of Relativity

• Suppose a ball is

thrown parallel to the

floor of a stationary

spaceship in a gravity-

free region.

• The ball would be

observed to follow a

straight-line path

according to Newton’s

first law.

The General Theory of Relativity

• If the spaceship were

accelerating at 9.8 m/s2,

the astronaut would

observe the ball to follow a

curved path to the floor.

• An outside observer would

see the ball moving in a

straight-line and the floor

of the spaceship

accelerates up to the ball.

The General Theory of Relativity

• Now let’s replace the ball with a beam of light.

• If the astronaut shines a flashlight at the far wall, and the spacecraft is at rest, then you will see the beam of light travel in a straight horizontal line.

The General Theory of Relativity

• If the spacecraft is accelerating upward, then the beam will follow a curved path downward relative to you.

• But if the beam of light curves in the accelerating elevator, then the equivalence principle says that the beam of light should also follow a curved path in a gravitational field.

Spacetime

• Light travels along the shortest path between two points in spacetime (a geodesic).

• A geodesic is the shape of the item.

• If the geodesic is curved, then the path of light is curved.

• Einstein proposed in his General Relativity theory that what is called gravity is really the result of curved spacetime.

Spacetime

• Time and space are relative to the motion

of an observer and they are not

independent of each other.

• Time and space are connected to make

four-dimensional spacetime (three

dimensions for space and one dimension

for time).

Spacetime

• This is not that strange---we often define

distances by the time it takes light to travel

between two points.

• For example, one light year is the distance

light will travel in a year. To talk about an

event, you will usually tell where (in space)

and when (in time) it happened. The event

happened in spacetime.

Spacetime

• The Earth does not orbit the Sun because the

Sun is pulling on it. The Earth is simply following

the shortest path in four-dimensional spacetime.

• If you have ever taken a long flight, you probably

already know that the shortest distance between

two cities is not a straight line. Non-stop flights

from the United States to Europe fly over parts of

Greenland. On a flat map the plane's flight path

looks curved, but on a globe, that path is the

shortest one!

Spacetime

• Light travels along a geodesic path between two

points in spacetime. Far from any gravity source,

the shortest distance is a straight line in three-

dimensional space.

• Near a massive object, the shortest distance is

curved in three-dimensional space. Stephen

Hawking gives the nice analogy that what we see

is like the curved motion of a shadow on the

ground from a plane flying in a straight line over

hilly terrain.

Spacetime

• In weak gravity conditions, the curvature of

spacetime is so small that Newton's law of

gravity works just fine.

• For very strong gravitational fields,

Newton's description of gravity becomes

inadequate. Einstein's theory of General

Relativity must be used to describe the

gravitational effects.

Einstein Equations • Since the mathematics of Newton's laws of motion and gravity are simpler than for Einstein's relativity theories, scientists prefer to use Newton's law of gravity for understanding interactions of slow-moving objects in any weak gravity field.

Evidence of Warped Spacetime

• A scientific theory must make testable

predictions which are tested through

observations and experiments.

• Prediction: Light passing close to a

massive object should be noticeably bent.

• The amount of bending increases as the

mass increases.

Evidence of Warped Spacetime

• Observation: During a solar eclipse you see that the stars along the same line of sight as the Sun are shifted ``outward''.

• This is because the light from the star behind the Sun is bent toward the Sun and toward the Earth. The light comes from a direction that is different from where the star really is.

Evidence of Warped Spacetime

• Observation: The light from quasars is observed to be bent by gravitational lenses produced by galaxies between the Earth and the quasars.

• It is possible to see two or more identical images of the same background quasar.

Evidence of Warped Spacetime

• Here is a picture from the

Hubble Space Telescope

showing the lensing of a

background galaxy by a

cluster of galaxies in front.

• The distorted blue arcs

visible around the center of

the picture are the lensed

background galaxy.

Evidence of Warped Spacetime • Signals from the Viking Lander on Mars were delayed when Mars was on the far side of the Sun.

• This is because it had to pass through the gravitational field (space-time warp) of the Sun.

• Using Einstein’s equations, the time difference is accounted for.

Evidence of Warped Spacetime

Prediction: Light escaping from a large mass

should lose energy---the wavelength must

increase since the speed of light is constant.

Stronger surface gravity produces a greater

increase in the wavelength.

Evidence of Warped Spacetime

• Observation: Spectral lines from the top layer of white dwarfs are significantly shifted by an amount predicted for compact solar-mass objects.

• The white dwarf must be in a binary system with a main sequence companion so that the amount the total shift due to the ordinary Doppler effect can be determined and subtracted out.

Evidence of Warped Spacetime Prediction: Objects with mass should create

ripples in the surrounding spacetime as they

move, called gravitational waves.

These waves do not travel through spacetime,

but are the oscillations of spacetime itself!

The spacetime ripples move at the speed of

light. However, the waves are very small and

extremely hard to detect.

Evidence of Warped Spacetime • Observation: Even the most sensitive detectors have not yet directly detected the tiny stretching-shrinking of spacetime caused by a massive object moving.

• However, the decaying orbits of a binary pulsar system discovered in 1974 by Russell Hulse and Joseph Taylor can only be explained by gravity waves carrying away energy from the pulsars as they orbit each other.

• This observation provides a very strong gravity field test of General Relativity.

Evidence of Warped Spacetime

• The two pulsars in the binary system orbit each other very rapidly with a period of only 7.75 hours in very eccentric and small elliptical orbits that bring them as close as 766,000 kilometers and then move them rapidly to over 3.3 million kilometers apart.

• Because of their large masses and rapidly changing small distances, the gravity ripples should be noticeable.

Evidence of Warped Spacetime

• Hulse and Taylor discovered that the orbit

speed and separation changes exactly in

the way predicted by General Relativity.

• They were awarded the Nobel Prize in

physics for this discovery.